diff --git a/server/conn.go b/server/conn.go
index 41133a9bec358..44f43920a8b37 100644
--- a/server/conn.go
+++ b/server/conn.go
@@ -1111,6 +1111,8 @@ func (cc *clientConn) Run(ctx context.Context) {
 	// by CAS operation, it would then take some actions accordingly.
 	for {
 		// Close connection between txn when we are going to shutdown server.
+		// Note the current implementation when shutting down, for an idle connection, the connection may block at readPacket()
+		// consider provider a way to close the connection directly after sometime if we can not read any data.
 		if cc.server.inShutdownMode.Load() {
 			if !cc.ctx.GetSessionVars().InTxn() {
 				return
diff --git a/tidb-server/main.go b/tidb-server/main.go
index e5ead347a1841..c816e5254508b 100644
--- a/tidb-server/main.go
+++ b/tidb-server/main.go
@@ -836,17 +836,15 @@ func closeDomainAndStorage(storage kv.Storage, dom *domain.Domain) {
 	terror.Log(errors.Trace(err))
 }
 
+// The amount of time we wait for the ongoing txt to finished.
+// We should better provider a dynamic way to set this value.
 var gracefulCloseConnectionsTimeout = 15 * time.Second
 
-func cleanup(svr *server.Server, storage kv.Storage, dom *domain.Domain, graceful bool) {
+func cleanup(svr *server.Server, storage kv.Storage, dom *domain.Domain, _ bool) {
 	dom.StopAutoAnalyze()
 
-	var drainClientWait time.Duration
-	if graceful {
-		drainClientWait = 1<<63 - 1
-	} else {
-		drainClientWait = gracefulCloseConnectionsTimeout
-	}
+	drainClientWait := gracefulCloseConnectionsTimeout
+
 	cancelClientWait := time.Second * 1
 	svr.DrainClients(drainClientWait, cancelClientWait)